Exit cycling for the Van der Pol oscillator and quasipotential calculations

We discuss the phenomenon of cycling for noise induced escape to a unstable periodic orbit. The presence of cycling is shown to follow from qualitative properties of two quasipotential functions. A method of numerically evaluating these quasipotential functions is described, and applied to the Van der Pol oscillator as an example. Figures resulting from these calculations reveal that nonconvergent cycling of exit measures does occur for the Van der Pol example.